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Repeated measures and two-factor ANOVA

Repeated measures and two-factor ANOVA. Chapter 14. Two extensions of ANOVA. Repeated measures: comparable to paired samples t-test Used with within-subjects design Factorial ANOVA: used when there is more than one predictor variable. Repeated measures ANOVA.

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Repeated measures and two-factor ANOVA

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  1. Repeated measures and two-factor ANOVA Chapter 14

  2. Two extensions of ANOVA • Repeated measures: comparable to paired samples t-test • Used with within-subjects design • Factorial ANOVA: used when there is more than one predictor variable

  3. Repeated measures ANOVA • Captures variability between conditions, compared to error •  MSbetween/MSerror • MSerror = variability within groups, with variability due to individual idiosyncrasies removed

  4. Calculating MSbetween • Just like in between subjects ANOVA • = SSbetween/df between • SSbetween = SStotal – SS within groups • df between = df total – df within

  5. Calculating MSerror • Variability within groups, minus variability due to individual people • SS within (calculated just like in between subjects ANOVA) minus… • SS between people (calculate mean for each person, across all treatments, and then calculate SS for those means) • SS error = SS within – SS between

  6. What about df error? • df error = df within – df between participants • df within = sum of df within each condition • df between participants = number of participants - 1

  7. So, MS error =… • SS error/df error • Bottom line: captures how much variability there is in scores that’s not just due to participants being unique weird people •  MS error < MS within • F = MS between/MS error •  repeated measures ANOVAs will have a better chance at detecting variability that’s due to condition

  8. What about effect size? • Still measured by h2 • Calculated by SS between conditions/(SS total – SS between participants) • Sometimes called partial h2, since individual differences are removed

  9. What about post hocs? • Still needed • Can use Tukey and Scheffe, just using MS error instead of MS within

  10. Bottom line • Repeated measures ANOVA captures the same idea as between subjects ANOVA • However, since the same participants are in each condition, individual differences can be removed from the equation •  more ability to detect differences due to condition

  11. The power of interactions • Sometimes one variable isn’t enough to capture what’s going on • Sometimes the role of one variable may differ, depending on the value of another variable •  interaction

  12. Types of interactions • Especially if: an effect is especially pronounced in some circumstances • Only if: an effect is only present in some circumstances • But if: the direction of an effect changes, depending on circumstances

  13. Three things to look for • Main effect: role of one variable in the dependent variable • Main effect (2): role of the other variable in the dependent variable • Interaction: does the role of one variable depend on the value of the other variable?

  14. To keep in mind • Once you have a significant interaction, you cannot interpret the main effects without taking that interaction into account

  15. Be sure you know • When to use repeated measures ANOVA • When to use factorial ANOVA • The general logic of each

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